Multiscale Topology of the Spectroscopic Mixing Space: Crystalline Substrates

Christopher Small^1*Daniel Sousa²

• ¹Lamont Doherty Earth Observatory, Columbia Climate School, Columbia University, Palisades, United States
• ²San Diego State University, San Diego, California, United States

The statistical and topological properties of spectral feature spaces are direct expressions of the populations of spectra they represent. Characterization of the topology and dimensionality of spectral feature spaces provides both quantitative and qualitative insight into their information content. Understanding the characteristics and information content of a spectral feature space is essential to modeling and interpretation of the target properties of spectra. The reflectance of crystalline substrates, specifically sands and evaporites, is of immediate relevance to remote sensing of the diversity of soils and terrestrial substrates more generally. The objective of this analysis is to characterize the topology and spectral dimensionality of spectroscopic feature spaces composed of a diversity of co-occurring sands and evaporites worldwide. To achieve this, we construct a composite spectral feature space as a mosaic of 30 desert environments imaged by NASA's EMIT spaceborne imaging spectrometer and compare the global and local structure of the aggregate spectral feature space using a combination of linear and nonlinear dimensionality reduction. The 3D (> 99%) variance partition of the EMIT mosaic suggests indicates that the spectral diversity of sand and evaporite reflectances is determined primarily by albedo and spectral continuumrelated to mineralogy, moisture content and illumination geometry. The spectral feature space defined by the low order principal components clearly distinguishes low and high albedo sand endmembers with multiple internal clusters indicating distinct spectral continuum shapes. The same feature space also contains a continuum of evaporite endmembers with no apparent clustering but a strong dependence of albedo and continuum curvature on moisture content. In contrast, 2D and 3D UMAP embeddings of the same feature space clearly distinguish at least 18 spectrally separable clusters interspersed amidst two continua of tendrils. One continuum is associated with multiple sand albedo gradients in the Gobi Desert while the other corresponds to a variety of low albedo basement outcrops in multiple granules. Together, these observations indicate that the EMIT spectrometer is able to clearly distinguish spectrally separable reflectance features in both the spectral continuum and narrowband absorptions, suggesting that the geographically distinct crystalline substrates included in the study are mineralogically distinct and completely spectrally separable.